86x − 43y + 2ax − ay = (86x − 43y) + (2ax − ay) = 43(2x − y) + a(2x − y) = (2x − y)(43 + a)

10by − 25bx − 6ay + 15ax = (10by − 25bx) − (6ay − 15ax) = 5b(2y − 5x) − 3a(2y − 5x) = (2y − 5x)(5b − 3a)

$x^2+xy-xz-yz=(x^2+xy)-(xz+yz)=x(x+y)-z(x+y)=(x+y)(x-z)$

$m^4+2-m-2m^3=(m^4-2m^3)+(2-m)=m^3(m-2)-(m-2)=(m-2)(m^3-1)=(m-2)(m-1)(m^2+m+1)$

$5a^2-5ab+5b^2-5ab=(5a^2-5ab)+(5b^2-5ab)=5a(a-b)+5b(b-a)=5a(a-b)-5b(a-b)=(a-b)(5a-5b)=5(a-b)(a-b)=5(a-b{)}^2$

$y-y^2-y^3+y^4=(y-y^2)-(y^3-y^4)=y(1-y)-y^3(1-y)=(1-y)(y-y^3)=y(1-y)(1-y^2)=y(1-y)(1-y)(1+y)=y(1-y{)}^2(1+y)$

$b^3+b^{2}c-b^{2}d-bcd=(b^3+b^{2}c)-(b^{2}d+bcd)=b^2(b+c)-bd(b+c)=(b+c)(b^2-bd)=b(b+c)(b-d)$

$x^{2}y-z^{2}x+y^{2}x-y{z}^2=(x^{2}y+y^{2}x)-(z^{2}x+y{z}^2)=xy(x+y)-z^2(x+y)=(x+y)(xy-z^2)$